A relaxation two-step Newton-based matrix splitting (RTNMS) iteration method is proposed to solve the generalized absolute value equations associated with circular cones (CCGAVE). The convergence of the RTNMS iteration method is investigated under suitable conditions. Numerical results illustrate that the RTNMS iteration method is feasible and effective for solving the CCGAVE. Moreover, some sufficient conditions for the unique solvability of the CCGAVE are given.